Simplify the following expression: $\dfrac{110k^5}{10k^4}$ You can assume $k \neq 0$.
Solution: $ \dfrac{110k^5}{10k^4} = \dfrac{110}{10} \cdot \dfrac{k^5}{k^4} $ To simplify $\frac{110}{10}$ , find the greatest common factor (GCD) of $110$ and $10$ $110 = 2 \cdot 5 \cdot 11$ $10 = 2 \cdot 5$ $ \mbox{GCD}(110, 10) = 2 \cdot 5 = 10 $ $ \dfrac{110}{10} \cdot \dfrac{k^5}{k^4} = \dfrac{10 \cdot 11}{10 \cdot 1} \cdot \dfrac{k^5}{k^4} $ $\phantom{ \dfrac{110}{10} \cdot \dfrac{5}{4}} = 11 \cdot \dfrac{k^5}{k^4} $ $ \dfrac{k^5}{k^4} = \dfrac{k \cdot k \cdot k \cdot k \cdot k}{k \cdot k \cdot k \cdot k} = k $ $ 11 \cdot k = 11k $